Superposition Benchmark Crack Full __link__ May 2026

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Title

Superposition Benchmark for Full-Field Crack Solutions in Linear Elastic Fracture Mechanics While searching for a "full crack" of the

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Abstract

This paper presents a benchmark problem for evaluating superposition-based numerical methods used in crack analysis. The infinite plate with a center crack under far-field tension (Mode I) is solved using the Williams stress function superposition principle. A "full" solution — including singular, constant, and regular terms — is derived analytically. Numerical methods (XFEM, BEM, FEM with enriched elements) are benchmarked against this exact solution for displacement and stress fields. The benchmark quantifies errors in stress intensity factor (SIF) and near-tip field accuracy. Results show that superposition of at least the first three Williams terms is required for full-field convergence within 1% error. The benchmark is provided as an open-source reference for code validation.

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  1. Finite Element Method (FEM): A commercial FEM software is used to model the plate with a central crack. The mesh consists of quadratic elements with a refined mesh around the crack tip.
  2. Extended Finite Element Method (XFEM): An XFEM implementation is used to model the crack growth using a phantom node approach.
  3. Boundary Element Method (BEM): A BEM code is employed to solve the problem using a collocation method.